Identifies all groups of nodes that are connected to each other in an undirected graph. Can be found using BFS or DFS.

Finds the minimum spanning tree of a weighted undirected graph using a greedy algorithm. Starts from an arbitrary node and grows the tree by adding the cheapest edge.

Orders nodes in a Directed Acyclic Graph such that every directed edge goes from earlier to later in the ordering. Essential for task scheduling and dependency resolution.

Finds shortest paths between all pairs of nodes in a weighted graph. Uses dynamic programming and works with negative weights (but not negative cycles).

Finds the minimum spanning tree by sorting all edges by weight and greedily adding edges that don't create a cycle. Uses Union-Find data structure.

DFS-based topological ordering: run DFS and push each node to a stack on completion. Reverse of the completion order gives a valid topological ordering.